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An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

机译:一种有效的递归分区方法,用于在矩形中打包相同的矩形

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摘要

In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes. Journal of the Operational Research Society (2010) 61, 306-320. doi: 10.1057/jors.2008.141 Published online 4 February 2009
机译:在这项工作中,我们处理矩形中包装(正交和不重叠)的问题(正交和不重叠)。这个问题出现在不同的物流设置中,例如托盘上的盒子装载,卡车中的托盘的安排以及船上的货物。我们提出了一种递归的分区方法,将改进版本的递归五块启发式和L-方法组合在较大的矩形和L形块中填充矩形。合并的方法能够快速找到托盘装载问题的所有实例的最佳解决方案集盖I和II(超过50000个实例)。如果与文献中的其他方法相比,解决问题集盖III(几乎100 000实例)和实际示例也是有效的。还讨论了一些理论结果,并基于它们,介绍了有效的计算机实现。计算机实现和数据集可用于基准测试。 “运营研究协会”(2010)61,306-320。 DOI:10.1057 / JORS.2008.141在线发布于2009年2月4日

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